Question

if a and b are the measures of two first quadrant angles and sin a = 4/5 and sin b = 5/13, find sin a+b.

Answer 1

[A] sin(a + b) =
`(63)/(65)`

Answer 2

given that sin a= 4/5
cos a= √(1-sin²a)
= √(1-16/25)
= √(9/25)
= 3/5
sin b=5/13
cos b= √(1-sin²b)
= √(1-25/169)
= √(144/169)
= 12/13

sin(a+b)= sin a· cos b + cos a · sin b
= 4/5· 12/13 + 3/5· 5/13
= 48/65+15/65
= 63/65
hope it helps